Complete controllability of finite-level quantum systems

Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we investigate the question of complete controllability for finite-level quantum systems subject to a single control field, for which the interaction is of dipole form. Sufficient criteria for complete controllability of a wide range of finite-level quantum systems are established and the question of limits of complete controllability is addressed. Finally, the results are applied to give a classification of complete controllability for four-level systems.Comment: 14 pages, IoP-LaTe

Control of non-controllable quantum systems: A quantum control algorithm based on Grover iteration

A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control algorithm based on Grover iteration is designed to perform a quantum control task of steering a system, which is eigenstate controllable but may not be (strongly) completely controllable, from an arbitrary state to a target state.Comment: 7 pages, no figures, submitte

Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly.Comment: 5 pages, orginal June 30, 2000, revised September 28, 200

Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography

We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy data. Here we show how to generalize this approach to systems with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the process for a range of three-level quantum systems. The results suggest that the Bayesian estimation of the frequencies and dephasing rates is generally highly accurate and the main source of errors are errors in the reconstructed Hamiltonian basis.Comment: 6 pages, 3 figure

Degrees of controllability for quantum systems and applications to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio

On the Contractivity of Hilbert-Schmidt distance under open system dynamics

We show that the Hilbert-Schmidt distance, unlike the trace distance, between quantum states is generally not monotonic for open quantum systems subject to Lindblad semigroup dynamics. Sufficient conditions for contractivity of the Hilbert-Schmidt norm in terms of the dissipation generators are given. Although these conditions are not necessary, simulations suggest that non-contractivity is the typical case, i.e., that systems for which the Hilbert-Schmidt distance between quantum states is monotonically decreasing form only a small set of all possible dissipative systems for N>2, in contrast to the case N=2 where the Hilbert-Schmidt distance is always monotonically decreasing.Comment: Major revision. We would particularly like to thank D Perez-Garcia for constructive feedbac

Complete controllability of quantum systems

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio

Optimal Control of One-Qubit Gates

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy spent in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions.Comment: 5 page

Clinical and functional characterisation of a novel TNFRSF1A c.605T > A/V173D cleavage site mutation associated with tumour necrosis factor receptor-associated periodic fever syndrome (TRAPS), cardiovascular complications and excellent response to etanercept treatment.

Objectives: To study the clinical outcome, treatment response, T-cell subsets and functional consequences of a novel tumour necrosis factor (TNF) receptor type 1 (TNFRSF1A) mutation affecting the receptor cleavage site. Methods: Patients with symptoms suggestive of tumour necrosis factor receptor-associated periodic syndrome (TRAPS) and 22 healthy controls (HC) were screened for mutations in the TNFRSF1A gene. Soluble TNFRSF1A and inflammatory cytokines were measured by ELISAs. TNFRSF1A shedding was examined by stimulation of peripheral blood mononuclear cells (PBMCs) with phorbol 12-myristate 13-acetate followed by flow cytometric analysis (FACS). Apoptosis of PBMCs was studied by stimulation with TNFa in the presence of cycloheximide and annexin V staining. T cell phenotypes were monitored by FACS. Results: TNFRSF1A sequencing disclosed a novel V173D/ p.Val202Asp substitution encoded by exon 6 in one family, the c.194–14G.A splice variant in another and the R92Q/p.Arg121Gln substitution in two families. Cardiovascular complications (lethal heart attack and peripheral arterial thrombosis) developed in two V173D patients. Subsequent etanercept treatment of the V173D carriers was highly effective over an 18-month follow-up period. Serum TNFRSF1A levels did not differ between TRAPS patients and HC, while TNFRSF1A cleavage from monocytes was significantly reduced in V173D and R92Q patients. TNFa-induced apoptosis of PBMCs and T-cell senescence were comparable between V173D patients and HC. Conclusions: The TNFRSF1A V173D cleavage site mutation may be associated with an increased risk for cardiovascular complications and shows a strong response to etanercept. T-cell senescence does not seem to have a pathogenetic role in affected patients